Conformal Geometry

Miao Jin received her PhD from the State University of New York at Stony Brook in 2008. She is the recipient of a National Science Foundation Career Award (2011-2016) for her work in computational conformal and quasi-conformal geometry, and is currently an Associate Professor at the University of Louisiana at Lafayette. Her research interests include computational geometry and topology, and especially computational conformal geometry, computational hyperbolic geometry, and computational quasi-conformal geometry - with applications to computer graphics, wireless sensor networks, geometric modelling, and computer vision. David Xianfeng Gu received his PhD from Harvard University in 2003. He is currently an Associate Professor at the State University of New York at Stony Brook and was an Assistant Professor at the University of Florida (2003-2004). His research interests include differential geometry, algebraic topology, Riemann surface theory and especially computational conformal geometry - with applications to computer graphics, computer vision, medical imaging, and scientific computing. He is the recipient of a National Science Foundation Career Award (2004-2009), Morningside Gold Medal in Applied Mathematics (2013) for his work in computational conformal geometry.

Introduction.- Topological Algorithms.- Harmonic Map.- Harmonic and Holomorphic Forms.- Discrete Ricci Flow.- Computer Graphics.- Computer Vision.- Geometric Modeling.- Medical Imaging.- Wireless Sensor Networks.

"Such algorithms make conformal maps into a computational tool for subjects such as computer graphics, computer vision ... and wireless sensor networks. The authors develop each of these topics in detailed chapters that give the reader tools to apply the sophisticated geometry of conformal mappings. The abundant diagrams are helpful, and the level of rigor supports the topics well. This book is a valuable addition to a mathematics or computer science library serving graduate students and professionals." (J. McCleary, Choice, Vol. 56 (5), January, 2019)

“Such algorithms make conformal maps into a computational tool for subjects such as computer graphics, computer vision … and wireless sensor networks. The authors develop each of these topics in detailed chapters that give the reader tools to apply the sophisticated geometry of conformal mappings. The abundant diagrams are helpful, and the level of rigor supports the topics well. This book is a valuable addition to a mathematics or computer science library serving graduate students and professionals.” (J. McCleary, Choice, Vol. 56 (5), January, 2019)